Some aspects of physics Some aspects of physics beyond the SM at the LHC beyond the SM at the LHC PASCOS 2012 Merida, México Alberto Casas (IFT-UAM/CSIC, Madrid)
Main purposes of the LHC Main purposes of the LHC Great LHC performance excluding almost all the Probe Higgs mass range Mechanism Maybe a Higgs signal at Impresive LHC job excluding paradigmatic Look for BSM BSM scenarios No signal so far
Physics Beyond the Standard Model (BSM BSM) ): : Physics Beyond the Standard Model ( CMSSM NUHM MSSM Gauge-Med MSSM, ... SUSY String-inspired MSSM... NMSSM Low SUSY MSSM.... Extra Dimensions: ADD, R-S, ... Composite Higgs / Little Higgs...
Physics Beyond the Standard Model (BSM BSM) ): : Physics Beyond the Standard Model ( Dark Matter candidates Flavour violation Z ’ , W ’ , 4th generation, ... Others:
Two main strategies to constrain NP Two main strategies to constrain NP Direct searches (NP particles production) Fingerprints in the effective theory
SUSY SUSY Motivations: Beautiful symmetry, strongly suggested by string theories Elegant solution to the Hierarchy Problem
SUSY SUSY Nice features of SUSY (not designed for them) Gauge Unification Radiative EW breaking Natural candidate for DM LHC test beautiful... but maybe false!
SUSY production at LHC Highest cross-sections of SUSY production are normally gluino and/or squark pair- production
Typical SUSY signals decay along cascades with diverse topology Each cascade always gives an LSP ( ) among the final states Always producing ≥ 2 jets (with/without leptons) + E T
Typical SUSY signals Most direct search of SUSY: jets with high p T E T 0-N leptons
It is not not straightforward to translate LHC straightforward to translate LHC It is results into bounds in SUSY (MSSM) results into bounds in SUSY (MSSM) MSSM has ~ 100 independent parameters ! (most of them related to the unknown mechanism of SUSY and transmission to the observable sector): A usual strategy is to present the LHC data as constraints in the CMSSM
CMSSM CMSSM at M X EW breaking Typical Spectrum
LHC constraints on the CMSSM LHC constraints on the CMSSM Mostly from multijet + E T
LHC constraints on the CMSSM LHC constraints on the CMSSM Mostly from multijet + E T
Roughly speaking, For , then CMSSM is in trouble The reason is that with such large masses, the EW breaking is fine-tuned We cannot “ forget ” about the fine-tuning problem, since the main reason to consider Weak-Scale SUSY was to avoid the Hierarchy Problem (fine- tuning of EW breaking in the SM)
About fine- -tuning tuning About fine Note that receive radiative contributions from other soft terms along the running from M X to M EW : Unnatural fine-tuning unless
Actually, the fine-tuning problem is more general and severe tree-level contrib. valid for any MSSM ( ≤ M Z 2 ) fine-tuning in the EW breaking also fine-tuned unless you have a good reason for it maybe strings ? ( see Aparicio, Fine-tuning in most MSSMs Cerdeno, Ibanez, 2012 )
Arbey et al 2012
Quick estimate of the degree fine-tuning contains several contributions (depending on the BSM scenario) Take the largest one, say Then, the fine-tuning (degree of cancellation) is In the MSSM, for non-small tan β , This approximately coincides with the Barbieri-Giudice definition:
For i.e. SUSY is fine-tuned at ~ 1% Is the CMSSM, or even the general MSSM, dead ??
( Parenthesis..... We have used that Lower bounds on m h Lower bounds on M SUSY But the reverse is also true: Upper bounds on m h Upper bounds on M SUSY
10, 3, 1 140, 130, 120, 115 Cabrera, JAC, Delgado 2011
E.g. Implications for Landscape considerations
Relevant example: Split SUSY 150, 140, 130, 120, 115
....Parenthesis) For i.e. SUSY is fine-tuned at ~ 1% Is the CMSSM, or even the general MSSM, dead ??
We can be more precise about the situation and We can be more precise about the situation and prospects of the CMSSM by performing prospects of the CMSSM by performing Global fits of the CMSSM Global fits of the CMSSM Use all availble exp. information (dominated by LHC) Use all availble exp. information (dominated by LHC) ≡ to show favoured/ /disfavoured regions in the disfavoured regions in the to show favoured CMSSM parameter space CMSSM parameter space Frequentist approach Frequentist approach Bayesian approach Bayesian approach (these types of analysis can be followed for any BSM scenario, not only CMSSM)
Frequentist approach Frequentist approach Scan the parameter space of the CMSSM (or whatever model), evaluating the likelihood (based on the ) This leads to zones of estimated probability (inside contours of constant ) around the best fit points in the parameter space.
68% Buchmueller et al. 2012 95% 68% before Higgs signal 95% before Higgs signal
Bayesian approach Bayesian approach Given a model, defined by: And some Exp. data , you evaluate, using the Bayes Theorem, the probability density in the parameter space
Bayesian approach Bayesian approach Likelihood ( L ) prior Posterior (pdf) norm. parameters of the model constant Posterior: our state of knowledge about θ i after we have seen the data Likelihood: probability of obtaining the data if θ i are true Prior: what we know about θ i before seeing the data
68% preliminar 95%
After including DM constraints
Not only the CMSSM is fine-tuned at ~1%, but even if the model is true, the chances to be discovered at the LHC are decreasing dramatically. Some questions To which extent the problems of CMSSM remain in general MSSMs ? Are there natural way-outs (maybe beyond MSSM) ?
( Frequentist vs Bayesian approaches Based just on the likelihood: Frequentist It does not give It does not penalize fine-tunings Based on the likelihood Bayesian and the prior It does give It does penalize fine-tunings
Since naturalness arguments are deep down statistical arguments, one might expect that an effective penalization of fine-tunings arises from the Bayesian analysis itself. ...and this is really what happens. Cabrera, Ruiz de Austri, J.A.C. 09
Method: Instead solving in terms of and the other soft terms and, treat as another exp. data Approximate the likelihood as Likelihood associated to the other observables
Use to marginalize fine-tuning penalization !
In practice you pick up a Jacobian factor: In practice you pick up a Jacobian factor: J model-independent part ! It contains the fine-tuning penalization It penalizes large tan β ) It applies to any MSSM (not just CMSSM)
Not only the CMSSM is fine-tuned at ~1%, but even if the model is true, the chances to be discovered at the LHC are decreasing dramatically. Some questions To which extent the problems of CMSSM remain in general MSSMs ? Are there natural way-outs (maybe beyond MSSM) ?
Original motivations for the C MSSM Minimal CP and Flavour violation Simplicity (-> universality in the soft terms) ~ arises in some theoretically motivated scenarios (e.g. minimal SUGRA or Dilaton-dominated SUSY) Only the first one is robust Going beyond CMSSM is very plausible Does it solve the problems of the CMSSM?
Going beyond CMSSM Going beyond CMSSM Some present directions: Promote CMSSM pMSSM Definition of pMSSM: no new CP phases, flavor-diagonal sfermion mass matrices and trilinear couplings,1st/2nd generation degenerate and A-terms negligible, lightest neutralino is the LSP. (19 parameters) This includes the possibility of a lighter 3rd generation Also certain types of spectrum that can evade detection at LHC: - Heavy LSP small p T s - “ Squashed spectrum ”
Note however that The 3rd generation cannot be too light (for m h =125 GeV) fine-tuning ...unless you have a large enough tree-level m h - Low-scale SUSY go beyond MSSM - NMSSM and similar Arrange the SUSY spectrum to fool LHC is possible, but it sounds artificial
All this represents new challenges for the data analysis: Test pMSSM Test a light 3rd generation Test “ Squashed Spectrum ” or heavy LSP Detect heavy SUSY
Search for a light 3rd generation Look for direct stop or sbottom pair production or through gluino decays Still plenty of room for a 3rd generation
Test a “ Squashed Spectrum ” or heavy LSP The study of events with ET + jets + multileptons may play a crucial role to test these scenarios Detect heavy SUSY (heavy squarks and gluino) - Look in alternative channels, like chargino/neutralino. - Design new kinematic variables etc.
Simplified model interpretation This is an effective strategy to interpret the exp results without using a particular scenario (like CMSSM) A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches (...) of new physics. D. Alves et al, arXiv:1105.2838 E.g. direct squark or gluino decays are dominant if all the other masses have multi-TeV values. Of course additional complexity can be built in.
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